Eldest Sons

Probability Level 2

In a certain village, every family has exactly two children, where each child is equally likely to be a boy or a girl. What is the probability that a random boy is the eldest son in his family?

Note: An "eldest son" is a boy who does not have an older brother.

25% 67% 75% 50%

1 solution

Ratul Pan
Nov 20, 2015

There are 4 equally likely possibilities for the families:
2 boys (1 older, 1 younger)
2 girls
1 boy(older) 1 girl(younger)
1 girl(older) 1 boy(younger than sister, but elder since no younger brother)

Out of the 4 boys, 3 are elder boys. Therefore, across the population, $3/4 = 75\%$ will be elder boys.

the possibility of two twin boys ??

Nikhil Sharma - 5 years, 6 months ago

The answer should be 50%. Eldest means first born of a set of sibling.

Zhi Wei - 5 years, 6 months ago

In some cultures, the eldest means the oldest boy, even if he has an older sister.

Pedro Hissa - 5 years, 6 months ago

The question now says eldest son - it may have been edited.

Callum Farnden - 5 years, 6 months ago

Should this not be a probability question? We can't say for sure that 75% of the sons are eldest sons; nowhere in the question is it stated that we can't have all children be girls except for one son in the village. That would mean the one son is the only eldest son in the village, as well as the only son, meaning that the proportion is 100%.

As for your solution - I agree with it, were it a probability question. It simply is not valid, as the question is a universal statement, stating that the given ratio must hold true in all villages where every family has two children.

Andrew Leung - 5 years, 6 months ago

I agree with u...there could be only 1 family in the entire village...then what?..if there is a son in that family the answer is 100%...if in one family there are 2 boys, in other one 1 boy 1 girl, the answer is 66%...if 2 families with 4 boys, the answer is 50%...so the way this question was asked is not correct i suppose.

Muhammad Arif - 5 years, 6 months ago

According to Ratul: 2 boys (1 older, 1 younger) = 1 boy Older 2 girls 1 boy(older) 1 girl(younger) = 1 boy Older 1 girl(older) 1 boy(younger than sister, but elder since no younger brother)

Then how can be: "Out of the 4 boys, 3 are elder boys" ? it should be: Out of the 4 boys, 2 are elder boys. So the result will be 50%

Shyamal Bairagi - 5 years, 6 months ago

crap question

Joshua Coddington - 5 years, 6 months ago

This solution is dependent on the definition of "eldest son" that was given. Had the definition not been given, the assumption of "eldest" as described in the comments would have prevailed.

Paul Wanger - 5 years, 6 months ago

Eldest Sons

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